# Linear Equation

• Feb 12th 2011, 10:44 AM
Naples
Linear Equation
Find the general solution of the given differential equations, the largest interval over which the solution is defied and determine whether there are any transient terms in the solution.

I mainly need someone to check my answer and if they're wrong to help me correct the mistakes I made
$dy/dx - 2y = x^2 + 5$
I found the integrating factor to be $e^-^2^x$
Multiplied both sides by integrating factor and integrated to get:
$e^-^2^xy = -1/2x^2e^-^2^x - 1/2xe^-^2^x - 5/2e^-^2^x + C$
$y = -x^2/2 - x/2 - 5/2 + Ce^2^x$

Largest interval I think would be (-∞, ∞) and I don't think there are any transient terms